This was the title given to Jacob,the son of Isaacafter he had struggled in a nocturnal fight with the angel of God. It is made up of two Hebrew words Isra-El meaning the fighter with (the angel of) God.
Gen 32:"28 And he said to him, What is your name? And he said, Jacob.29. And he said, Your name shall be called no more Jacob, but Isra-el; for as a prince you have power with God and with men, and have prevailed"
From then on, according to the Bible, all the descendants of Jacob - the twelve tribes and their progeny - were identified as the People Israel(Am Yisrael),Israelites.
*** The Quran, based upon Muhammad's misunderstanding - as usual - of the Hebrew language and traditions, created a separating barrier between the Israelites up to the death of Moses from those who followed his death including the Jews.
As far as Muhammad was concerned, the later followers of Moses - like the later followers of Jesus - were not the SAME as the earlier ones since they allegedly DISOBEYED and BROKE their COVENANT with ALLAH, not withstanding the fact that neither the Jews nor the Christians knew who Allah was since he was actually the supreme rock god of the Quraysh tribe in Mecca embedded in the corner wall of the Ka'ba called the BLACK STONE ***